Tiffany is 3 times as old as Emily. Fourteen years ago, Tiffany was 5 times as old as Emily. How old is Emily now?
Solution: We can use the given information to write down two equations that describe the ages of Tiffany and Emily. Let Tiffany's current age be $t$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $t = 3e$ Fourteen years ago, Tiffany was $t - 14$ years old, and Emily was $e - 14$ years old. The information in the second sentence can be expressed in the following equation: $t - 14 = 5(e - 14)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to use our first equation for $t$ and substitute it into our second equation. Our first equation is: $t = 3e$ . Substituting this into our second equation, we get: $3e$ $-$ $14 = 5(e - 14)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $3 e - 14 = 5 e - 70$ Solving for $e$ , we get: $2 e = 56.$ $e = 28$.